Parent object to bone latency (lag) issue
I searched the bug report and the file you provided there. There is indeed a dependency cycle on object level - it prints out into the system console:



The culprit is that the empty is parented to the head. Blender checks dependency cycles on object level in old dependency graph, which is a known limitation.

To solve the issue switch to the new dependency graph by running blender with --enable-new-depsgraph command line argument. It will work there, because blender evaluates dependencies better and on bone level.